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solutions2 - Homework Set 2 Due Wednesday 07/06 Problem 1 A...

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Homework Set 2 Due Wednesday, 07/06 Problem 1 A wave on a string has an amplitude of 1.5cm, a period of 0.12 seconds, and a wavelength of 1.1 meters. a. What is the wave's frequency, angular frequency, wave number and wave speed? b. If the string is under tension of 5.0N, what is its mass per unit length, in grams per meter? c. If the tension in the string changes to 10.0N but the frequency of the wave remains the same, what is its new wavelength? Solution: a. The frequency, angular frequency, wave number and wave speed are b. We know the wave speed from part (a) and are given the tension, so we can solve for the mass per unit length: c. First, determine how the wavelength depends on the tension, if the frequency is held fixed: The wavelength is therefore proportional to the square root of the tension. The tension is doubled, so the new wavelength is

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Problem 2 A string with mass per unit length μ = 10.0g/m is tied down on one side, and runs over a pulley on the other side, 0.30 meters away. The end that runs over the pulley is attached to a 1.5 kilogram mass. Assume that the end of the string that is tied down and the point that runs over the pulley cannot move, but the piece between these points is free to oscillate. a. What is the string's fundamental frequency? b. Now this system is placed in an accelerating elevator. The 3rd harmonic frequency is measured to be 204 hz. Is the elevator accelerating up or down? What is its acceleration? Solution: a. In the fundamental mode, half a wavelength fits on the string between x = 0 and x = L . Therefore, the wavelength is 0.60m. The wave speed is The frequency of the fundamental mode is then b. To figure out the acceleration, we need to know the effective gravity inside the elevator. We are given the frequency of the 3rd normal mode, which is equal to 3 times the frequency of the 1st mode. Use this to determine the wave speed: Since the apparent acceleration due to gravity inside the elevator is higher than g by 1.3m/s 2 , we know that the elevator is accelerating upward at 1.3m/s 2 .
Problem 3 Two strings with different masses per unit length are connected together and held at a tension of 50 N : An wave with an amplitude of 2.50cm and a frequency of 60.0 hz is incident from the left. The waves on the left-hand string are observed to have a wavelength of 30.0cm, while those on the right-hand string have a wavelength of 20.0cm. a. What is the mass per unit length, μ 1 , of the left string? What is the mass per unit length of the right string? b. What is the amplitude of the transmitted waves on the right string? c. What is the transmission coefficient? What is the reflection coefficient?

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